Kepler's achievements in mathematics would alone have been sufficient to win for him enduring fame; he first enunciated clearly the principle of continuity in mathematics, treating the parabola as at once the limiting case of the ellipse and the hyperbola, and showing that parallel lines can be regarded as meeting at infinity; he introduced the word 'focus' into geometry; while in his Stereometria Dolorum, published 1615, he applied the conception to the solution of certain volumes and areas by the use of infinitesimals, thus preparing the way for Desargues, Cavalieri, Barrow, and the developed calculus of Newton and Leibniz.
Johannes KeplerRelated topics
barrow calculus case certain conception continuity ellipse enduring fame focus geometry hyperbola infinity limiting mathematics meeting once parabola parallel preparing principle showing solution thus treating use way while win word leibniz newton linesRelated quotes
If... God highly exalted Christ because He humbled Himself, suffered dishonour, was tempted and endured a shameful cross and death for our sake, how will He save, glorify and raise us up if we neither choose humility, nor show love to our fellows, nor gain our souls by enduring temptation (cf. Lk. 21:19), nor follow the saving Guide through the 'strait gate' and along the 'narrow way' leading to eternal life (Mt. 7:14)? To this end we were called, says Peter, the chief Apostle, ' Because Christ also suffered for us, leaving us an example that we should follow His steps' (I Pet. 2:21).
Gregory Palamas
In 1800 he had published his momentous discovery of infra-red rays; and in 1803 and 1804 his re-examination of double stars would reveal examples where the two components had orbited each other, visual proof that attractive forces...operated outside the solar system. ...between 1811 and 1818 he published four great synthetic papers on the construction of the heavens, in which he expounded the life-story of nebulae and clusters as they developed over time under the influence of gravity. ...Soon, development over time-in contrast to the unchanging clockwork universe of Newton and Leibniz-would become and remain part of astronomical thinking.
William Herschel
Social work as a profession is of relatively recent origin. The first social welfare agencies appeared in urban areas in the early 1800s. These agencies, or services, were private and were developed primarily at the initiation of the clergy and religious groups. Until the early 1900s, these services were provided exclusively by the clergy and affluent "do-gooders” who had no formal training and little understanding of human behavior or of how to help people. The focus of these private services was on meeting such basic physical needs as food and shelter and on attempting to cure emotional and personal difficulties with religious admonitions.
Charles Zastrow
James Buchanan ... produced several seminal contributions to the literature prior to the appearance of The Calculus, and a continual stream of books and articles afterward. I view Buchanan's Nobel Prize as a reward for this great body of work, and not just limited to The Calculus. Pursuing this line of reasoning, Gordon Tullock's prodigious research output following the publication of The Calculus also justifies a Nobel Prize. Indeed, Tullock's (1967c) seminal analysis of rent seeking, and his subsequent work on this topic might be regarded as sufficient achievements for the awarding of a prize.
Dennis Mueller
I would like to focus your attention not on the subject of the article (national security in a nuclear world) but on the kind of conclusion they reached, namely that there is no technical solution to the problem. An implicit and almost universal assumption of discussions published in professional and semipopular scientific journals is that the problem under discussion has a technical solution. A technical solution may be defined as one that requires a change only in the techniques of the natural sciences, demanding little or nothing in the way of change in human values or ideas of morality.
Elinor Ostrom
